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Is this simple derivation of length contraction and time dilation corr

  1. Apr 29, 2013 #1
  2. jcsd
  3. Apr 30, 2013 #2

    ghwellsjr

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    I don't like the article. I don't like articles that say things like, "Unfortunately, the most confusing part is yet to come", as if it was already confusing but it's getting worse. Whenever you see a writeup that admits it is confusing, it's more than likely that the author is confused. And he is confused in the same way that a great many writers are confused. He is confused between what he sees and what the observers in his explanation see. He states that the observers see the Time Dilation of the other ones clock which is not true. We can see it because we are able to see every event in the scenario simultaneously but the observers in the scenario have to wait for the light from the events to propagate to them.

    So how does this bear out in the article? He talks about one observer seeing the other one flying past. Well if that is going to happen, then the first one will see the second ones clock ticking faster than his own while approaching and then suddenly switch to ticking slower than his own while departing. This is Relativistic Doppler which is what the observers see when looking at each others clock. They never see Time Dilation.

    He attributes the reciprocal Time Dilation to the Relativity Principle (Einstein's first postulate) which is not true. the Relativistic Doppler can be attributed to the Relativity Principle. At least he correctly points out that the Time Dilation is frame dependent but he shouldn't be saying that each observer sees things differently depending on whether they are at rest in their own frame (How could they not be? That's the accepted definition of "their own frame".)

    It's so easy to explain Time Dilation and what observers see that I have no tolerance for explanations that seem to relish confusing their readers.
     
  4. Apr 30, 2013 #3
    george,i somewhere in his article saw that he used old velocity addition for the "light" too.. Isn't that wrong? I think he used that in proving length contraction...
     
  5. Apr 30, 2013 #4
    george,then what is 'time dilation' according to you?
     
  6. Apr 30, 2013 #5

    ghwellsjr

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    I actually didn't read the length contraction part but I don't think there is anything wrong with regard to velocity addition. He's showing things from the point of view of the frame which is the correct way to do it but explains it from the point of view of the observers which is not something they can view.
     
  7. Apr 30, 2013 #6

    ghwellsjr

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    Time Dilation is the ratio of the passage of Coordinate Time to Proper Time for a clock moving in an Inertial Reference Frame (IRF). It is therefore frame dependent and not visible to any observer.

    I recently gave an explanation on a thread called Time Dilation with this post (#10):

    Since the OP didn't respond to my question if it was simple, maybe you could.
     
  8. Apr 30, 2013 #7
    the part that i think is wrong is that he used c+v and c-v which he shouldn't use.. As it violate second postulate of relativity..
    And do you know how to calculate relativistic doppler?? I think it will be very usefull to me if you can explain in simpler manner. It is a request from me...
     
  9. Apr 30, 2013 #8

    ghwellsjr

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    Perhaps a couple spacetime diagrams will help to illustrate his explanation of Length Contraction. First, the IRF for the rest frame of the train:

    attachment.php?attachmentid=56630&stc=1&d=1363147942.png

    The observer is shown in blue and her mirror is shown a measured six feet away in red. I'm showing just one cycle of a light pulse traveling from her to the mirror and back.

    Now, the IRF for the ground rest frame:

    attachment.php?attachmentid=56631&stc=1&d=1363147942.png

    Can you see that while the light is moving away from the observer on the train, it is going at c-v relative to the observer and after it reflects off the mirror it is going c+v?
     
  10. Apr 30, 2013 #9
    Yes,then why speed of light "appears" constant?
     
  11. Apr 30, 2013 #10
    George,why i said it violates 2nd postulate is that light is not treated like that way.. i.e.light moves at the velocity c+v relative to train in the direction of motion and light moves c-v in the direction opposite to that of train...

    This is a part of what Einstein said:

    """""""""Of course we must refer the process of the propagation of light (and indeed every other
    process) to a rigid reference-body (co-ordinate system). As such a system let us again
    choose our embankment. We shall imagine the air above it to have been removed. If a ray
    of light be sent along the embankment, we see from the above that the tip of the ray will be
    transmitted with the velocity c relative to the embankment. Now let us suppose that our
    railway carriage is again travelling along the railway lines with the velocity v, and that its
    direction is the same as that of the ray of light, but its velocity of course much less. Let us
    inquire about the velocity of propagation of the ray of light relative to the carriage. It is
    obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage. The velocity w of
    the man relative to the embankment is here replaced by the velocity of light relative to the
    embankment. w is the required velocity of light with respect to the carriage, and we have
    w = c-v.
    The velocity of propagation ot a ray of light relative to the carriage thus comes cut
    smaller than c.
    But this result comes into conflict with the principle of relativity set forth in Section V."""""""""""

    light appears moving in less velocity is not allowed..
     
  12. Apr 30, 2013 #11

    ghwellsjr

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    It depends on what you are asking.

    If you are asking why the speed of light measures to be a constant (a result of Einstein's first postulate, the Principle of Relativity), then the above two diagrams illustrate that. In both cases the observer sends out a light pulse at his time of 4 nanoseconds and detects the reflection from the mirror that he measured to be six feet away at his time of 16 nanoseconds. So the light, as far as he is concerned traveled 12 feet (round-trip) in 12 nanoseconds which is 1 foot per nanosecond. When we measure the speed of light, it is always a round-trip measurement and we cannot tell if the two trips are the same as in the first IRF or different as in the second IRF.

    But if you are asking about the stipulation that light propagates at c in any IRF (Einstein's second postulate) then that is something that does not appear to us. We cannot observe the propagation of light. We can't know what it is unless we define it in some way and that's what the second postulate does for us. You can see that in any IRF that I draw. The light signals always travel along 45 degree diagonals which in this case is 1 foot per nanosecond. We can see it in our diagrams but the observers in our diagrams cannot tell whether we are using the first IRF or the second IRF, both of which have the light traveling at c but they can't tell if the light takes the same amount of time to get to the mirror as it takes for the reflection to get back to them.
     
    Last edited: Apr 30, 2013
  13. Apr 30, 2013 #12

    ghwellsjr

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    You need to read to the end of the chapter and then subsequent chapters.
     
  14. Apr 30, 2013 #13
    So in reality light travels in different speeds but we aren't able to detect them because of time dilation and length contraction..right?? Now,i find that it is similar to absolute frame of reference...

    I feel like there is absolute frame of reference due to this...
     
  15. Apr 30, 2013 #14
    Well,i have already read it 2 to 3 times and i think light travelling at different velocities is the reason for simultaneous events being non-simultaneous and vice-versa..
     
  16. Apr 30, 2013 #15
    And Einstein gave relationship..Time and Relativity of simultaneity.. They are closely linked to each other... Since Simultaneity changes in different frames(base on relative motion) because of light,light travelling at different velocities in different frames is the reason for time dilation and length contraction..
     
  17. Apr 30, 2013 #16
    What about half-way?? here we considered two-ways,that is why light speed is measured constant.what about half-way? How light appears constant?
     
  18. Apr 30, 2013 #17

    ghwellsjr

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    The formula for Relativistic Doppler is:

    √((1+β)/(1-β))

    where β is the approaching speed as the ratio v/c.

    For a departing speed it is simply the inverse of the above.

    So in the second IRF shown for Time Dilation, β = 0.6 so:

    √((1+β)/(1-β)) = √((1+0.6)/(1-0.6)) = √(1.6/0.4) = √4 = 2

    This means that while approaching at 0.6c, each observer will see the other ones clock ticking twice as fast as their own and while departing at that speed, they will each see the other ones clock ticking at half the rate of their own.

    Unlike Time Dilation for which each clock/observer/object is independent of all the others and has a Time Dilation dependent only on their individual speeds in the IRF, Relativistic Doppler is an effect between two inertial clocks/observers/objects. So I have added a stationary red observer in the second IRF from above. First I show the light signals sent each nanosecond from the traveling blue observer:

    attachment.php?attachmentid=58359&stc=1&d=1367312818.png

    Note how in the bottom of the diagram, while the blue observer is approaching the red observer, the red observer sees two ticks of blue's clock for every one of his own. Then after they cross paths while they are departing, red sees blue's clock ticking at one-half the rate of his own.

    Now what does blue see of red's clock?

    attachment.php?attachmentid=58360&stc=1&d=1367312818.png

    Same thing--even though we are only using one IRF in which red is at rest.

    And please note that the Time Dilation factor of 1.25 is not observable by either observer, only the Relativsitc Doppler factors are.
     

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    Last edited: Apr 30, 2013
  19. Apr 30, 2013 #18
    My Guess of relativistic Doppler was absolutely right!! I understood from your comment.. Thank you!!
     
  20. Apr 30, 2013 #19

    ghwellsjr

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    When we define light to travel in an IRF at c in all directions, it is identical to what scientists believed was the case for a single unknown IRF.

    Maybe it would be helpful for you to read the first few sections of Einstein's first paper on SR. It's much shorter and gets right to the point.

    I hope I'm understanding what you mean by this-that comparing one IRF to another, light is traveling at different speeds relative to the observers/objects/clocks, correct? But you should only think of one IRF at a time and say that light travels at c in that IRF. To get to another IRF, you use the Lorentz Transformation to convert all the coordinates of the events in the first IRF to the second IRF and then you don't mix any coordinates between them.

    I think by half-way, you mean what I mean by one-way. Each "half" of the round-trip is a one-way trip so the two one-way trips add up to the round-trip.
     
  21. Apr 30, 2013 #20
    WOW!! exactly!! isn't that correct???
     
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